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Chapter 6

Test Yourself

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03:32

Find the volume of a spher…

00:48

A sphere is inscribed in a…

00:29

The surface area of a cube…

01:15

Find (a) the volume and (b…

01:21

Find the volume of each pr…

01:05

00:56

What is the volume of a su…

04:07

A box has an open top, rec…

00:40

Find the missing dimension…

01:29

The volume of a rectangula…

can, this one says. What is the volume in cubic inches of acute, whose total surface area is two hundred and sixteen square inches? First of all, let's think about the equation for the surface area of a cute for a service area. If it's a queue, you know that all the six sides are equal, so we could just take one of the sides areas and multiply that by six. So area on one side time. Six. So then what's the area of one side? We know that because it's a cube, it's actually just made up of six squares, which means it's just gonna be length times length, because the length and the width should be the same. So we could just call that length times width length when we know it's gonna be six l squared, and we know that the six all squared in this particular Kew is going to be two sixteen square inches. Co. Tells us that the total surface area there's two sixteen, so then we just have to first of all, isolate our l here. If we were to do that, we just have to divide both sides by six Look, which becomes thirty six. So another L squared is equal to thirty six. So from here we can try to get help by square routing both sides because this square in the square, it should cancel out. We should get that l. A is equal to six. So then I must think about the volume of a Q. So we know that the volume is just going to length times, width, times, height because we know length, width and height are all the same because it's a cute you could just you tell cute. So if we plug in that l that we found from our surface area into this equation, we should get six cute, and that should just be two sixteen. So we know actually that the volume and the surface area actually be the same for this one.

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